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Properties

Label 348726p
Number of curves $2$
Conductor $348726$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 348726p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
348726.p1 348726p1 [1, 0, 1, -93507, 10904170] [2] 2396160 \(\Gamma_0(N)\)-optimal
348726.p2 348726p2 [1, 0, 1, -24917, 26570126] [2] 4792320  

Rank

sage: E.rank()
 

The elliptic curves in class 348726p have rank \(1\).

Complex multiplication

The elliptic curves in class 348726p do not have complex multiplication.

Modular form 348726.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - 2q^{11} + q^{12} + 2q^{13} + q^{14} - 2q^{15} + q^{16} - 2q^{17} - q^{18} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.